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We consider the functional equation f(ax+y)+f(ax-y)-a(a + 1)f(x)-a(a - 1)f(-x)-[f(y)+f(-y)]+k[f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)]=0 for a fixed rational number a with a≠ 1, -1, 0 and a fixed real number k. We study the solution of the equation between linear spaces and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy normed space. [ABSTRACT FROM AUTHOR]

We investigate the following typical form of a certain class of quadratic functional equations: f(ax + by) + f(ax - by) + c[f(x + y) + f(x - y) - 2f(x) - 2f(y)] = 2a2f(x) + 2b2f(y). Furthermore, we provide a systematic program to prove the generalized Hyers-Ulam stability for the class of functional equations via the stability for the typical form. [ABSTRACT FROM AUTHOR]

We investigated the etch rate of indium gallium zinc oxide (IGZO) thin films and the selectivity of IGZO for SiO2 and Si in an inductively coupled plasma. The maximum etch rate of the IGZO thin film was 158 nm/min in BCl3/Ar (10:10 sccm) plasma, and the selectivity of IGZO for SiO2 and Si was 0.7 and 2.2, respectively. We analyzed the chemical reaction on the surface of the IGZO thin film via XPS analysis. Numerous byproducts, including GaxCly, InClx, and ZnClx, were generated in BCl3/Ar plasma during the etching of the IGZO thin film, and the non-volatile byproducts from the surface of the etched IGZO thin film were removed by Ar bombardment. Consequently, the etching mechanism of the IGZO thin film can be explained as a chemical reaction with the ion-assistance of Ar sputtering. [ABSTRACT FROM AUTHOR]

The ZrO2 thin film was investigated with the surface characteristics of ZrO2 thin films etched in the HBr/SF6 using Adaptively Coupled Plasma (ACP) system. The plasmas were characterized using optical emission spectroscopy (OES) analysis. The crystal structure of the films etched with various gases mixing ratio was observed by X-ray diffraction (XRD). These results can indentify the ion bombardment and chemical reaction for plasma damages at the crystalline structure of the ZrO2 surface. The chemical reactions of the etched ZrO2 films were investigated using X-ray photoelectron spectroscopy (AR-XPS). The etching mechanism of ZrO2 thin films could be explained as which Zr interacted with the Br and F radical by adding HBr, but remained at the surface due to non-volatility of ZrFx and ZrBry. From the experimental results, the etch mechanism of ZrO2 was ion-assisted chemical reaction. [ABSTRACT FROM AUTHOR]

In this study, the etching characteristics of HfAlO3 thin film were investigated by varying the etch parameters such as the gas mixing ratio, the radio frequency power, the direct current bias voltage, and the process pressure in an inductively coupled plasma. The maximum etch rate of HfAlO3 thin film and the selectivity of HfAlO3 to SiO2 were 20.55 nm/mm and 0.38 in the CF4/Cl2/Ar (2:6:14 sccm) plasma, respectively. The plasma was analyzed by using optical emission spectroscopy. The chemical states on the surfaces of the etched HfAlO3 thin film were investigated with X-ray photoelectron spectroscopy. The etching of HfAlO3 thin films is performed by the interaction of Hf and Al atoms with the Cl and F radical in the CF4/Cl2/Ar plasma. However, their byproducts were remained at the surface because Hf-F and Al-F were non-volatile. Therefore, the plasma etching of the HfAlO3 films follows the ion assisted chemical reaction. [ABSTRACT FROM AUTHOR]

In this study, the etch mechanism of ALD deposited Al2O3 thin film was investigated in BCl3/Cl2/Ar plasma. The experiments were performed by comparing etch rates and selectivity of Al2O3 over hard mask materials (such as SiO2, and Si3N4) as function of the input plasma parameters such as gas mixing ratio, DC-bias voltage and RF power under fixed process pressure. The maximum etch rate was obtained at 115.75 nm/min under 5 mTorr, RF power 600 W, Cl2 10% was added to BCl3/Ar plasma, and the highest etch selectivity was 1.17 over Si3N4 under the 10 mTorr process pressure, -50 V DC-bias voltage. We used the X-ray photoelectron spectroscopy (XPS) to investigate the chemical reactions on the etched surface. [ABSTRACT FROM AUTHOR]

In this study, etching characteristics of TaN for barrier-layer and SiO2 for hard mask were investigated by using the inductively coupled Cl2-based plasma. Dry etching of the TaN was studied by varying Cl2/Ar gas mixing ratio. The results showed that the best condition for the etch rate was at the Cl2 only gas plasma. The chemical reaction on the surface of the etched TaN was investigated with X-ray photoelectron spectroscopy (XPS). Scanning electron microscopy (SEM) was used to investigate the surface of etched TaN thin film. [ABSTRACT FROM AUTHOR]

We investigated etching behavior of ZrO2 thin films and selectivity of ZrO2 thin films to SiO2 and Si3N4 by using inductively coupled plasma system. Experimental results have shown that higher etch rate of ZrO2 thin films was achieved by the reactive ion etching using Cl radicals due to the high volatility of BxClyOz. Consequently, the increased chemical effect was caused to the increase in the etch rate of the ZrO2 thin film. Small addition of Cl2 to the BCl3/Ar mixture increased selectivities of ZrO2 thin films to SiO2 and Si3N4. The surface analysis by x-ray photoelectron spectroscopy (XPS) showed some evidences that Zr and O were reacted with Cl and BCl and formed nonvolatile metal chlorides and volatile boron-oxy-chlorides. This effect can be related to the concurrence of chemical and physical pathways in the ion assisted chemical reaction. [ABSTRACT FROM AUTHOR]

In this study, we carried out an investigation of the etching characteristics (etch rate, selectivity to Si) of ZrO2 thin films in the HBr/CF4 high density plasma (HDP) system. The maximum etch rate of 70.8 nm/min for ZrO2 thin films was obtained at HBr(75%)/ CF4(25%) gas mixing ratio. At the same time, the etch rate was measured as a function of the etching parameter such as HDP chamber pressure. The X-ray photoelectron spectroscopy (XPS) analysis showed an efficient destruction of the oxide bonds by the ion bombardment as well as an accumulation of low volatile reaction products on the etched surface. Based on these data, the ion-assisted chemical reaction was proposed as the main etch mechanism for the CF4-containing plasmas. [ABSTRACT FROM AUTHOR]

In this study, we changed two input parameters (pressure vs. gas mixing ratio, RF power and DC bias voltage) and then monitored the effect on HfO2 etch rate and selectivity with Si3N4 and SiO2. When the pressure was fixed at 5 mTorr, etch rate of HfO2 decreased with increasing Cl2 content from 0 to 30% in BCl3/Ar plasma. At the conditions of 10 and 15 mTorr, the HfO2 etch rate reached the maximum at 10% Cl2 addition. As RF power and DC bias voltage increased in all ranges of pressure conditions, etch rates for HfO2 showed increasing trends. The relative volume densities of radicals were monitored with optical emission spectroscopy (OES). The analysis of x-ray photoelectron spectroscopy (XPS) was carried out to investigate the chemical reactions between the surfaces of HfO2 and etch species. Based on experimental data, the ion-assisted chemical etching was proposed as the main etch mechanism for the HfO2 thin films in Cl2/BCl3/Ar plasma. [ABSTRACT FROM AUTHOR]

In this work, we investigated etching characteristics of HfO2 thin film and Si using inductive coupled plasma (ICP) system. The maximum etch rate of HfO2 is 85.5 nm/min at a BCl3/(Ar+BCl3) of 20% and decreased with further addition of BCl3 gas. From the QMS measurements, the most dominant positive ion energy distributions (IEDs) showed a maximum at 20% of BCl3. These tendency was very similar to the etch characteristics. This result agreed with the universal energy dependency of ion enhanced chemical etching yields. From the mass spectra, the Hf chloride and bromine oxide must be included in the etching by-products as volatile species. [ABSTRACT FROM AUTHOR]

The investigation of etch characteristics for (Na0.5K0.5)NbO3 (NKN) thin films in Cl2/Ar inductively coupled plasma was carried out. It was found that the NKN etch rate is a monotonic function of both input power and negative dc bias as it generally expected from the corresponding variations of plasma parameters. At the same time, NKN etch rate shows a non-monotonic behavior as a function of Cl2/Ar mixing ratio with a maximum of 750 Å/min at Cl2 (80%)/Ar (20%). The analysis of these data togeter with the XPS results for both as-deposited and etched NKN films allowed one to assume ion assisted etch mechanism and defined a concurence of chemical and physical etch pathways as a most probable reason for etch rate maximum. [ABSTRACT FROM AUTHOR]

Dielectric PST (20/80) / PST (80/20) heterolayered thin films structures were created by a consequent deposition of the PST (20/80) and PST (80/20) thin films on the Pt/Ti/SiO2/Si substrate using alkoxide-based sol-gel method. Both structural and dielectric properties of heterolayered PST thin films were investigated for the tunable microwave device applications. As the number of coating increases, the lattice distortion decreased. It can be assumed that the lower PST layer affects a nucleation site or a seeding layer for the formation of the upper PST layer. The dielectric constant, dielectric loss and tunability of the PST-6 heterolayered structure measured at 100 kHz were 399, 0.022 and 57.9%, respectively. All these parameters showed an increase with increasing number of coatings due to the decrease in lattice distortion. [ABSTRACT FROM AUTHOR]

The (NaxK1- x)NbO3 (NKN) thin films were fabricated by using the alkoxide-based sol-gel method. The NKN stock solution was spin-coated onto a Pt/Ti/SiO2/Si substrate. The coating and drying procedures were repeated several times to obtain the film thickness of about 200 nm, and then the films were annealed at 550-700°C for 1 h. Structural properties of the NKN thin films were investigated by thermogravimetric analysis/differential scanning calorimetry, field emission scanning electron microscope and X-ray diffraction spectroscopy. The dielectric constant and the dielectric loss for the films sintered at 650°C were found to be 338 and 0.018, respectively. The results show that the NKN thin films are promising candidate for use in tunable devices application. [ABSTRACT FROM AUTHOR]

This article describes the synthesis and the purification of carbon nanotubes. Large quantities of single-walled carbon nanotubes (SWNTs) with few defects and very small amount of amorphous carbon coating have been synthesized by catalytic decomposition of methane over well-dispersed iron particles supported on MgO at the temperature range from 800 to 1000 °C. It was found that the quality of carbon nanotubes was slightly increased as increasing growth temperature while the yield was decreased to some degree. It was also found that the as-grown SWNTs can be separated easily from the support by a simple acidic treatment rather than thermal oxidation to obtain a product with high yields of SWNTs. Above 94 wt % high purity SWNTs were obtained by combining two-step processes of thermal oxidation in air and acid treatment without multistep filtration. The as-grown and purified SWNTs were also characterized by field emission scanning electron microscopy, x-ray diffraction, and Raman spectroscopy. [ABSTRACT FROM AUTHOR]

The etching mechanism of (Bi4-xLax)Ti3O12 (BLT) thin films in Ar/Cl2 inductively coupled plasma (ICP) was investigated as a function of gas mixing ratios, process pressure, and ICP powers at fixed other conditions. Etch rates were measured by using an α-step surface profiler. The maximum etch rate of BLT thin films was 117 nm at 0.8 Ar/(Ar+Cl2) gas mixing ratios with following conditions: process pressure of 15 mTorr, gas flow rate of 20 sccm, ICP power of 700 W, and dc bias of -150 V. The etch rate was increased as decreasing the process pressure. For a detailed investigation of etching mechanisms of BLT thin films, the ion energy distributions of each positive species were measured using quadrupole mass spectrometer and analyzed those data. Also the electron energy distribution was measured as a function of Ar/Cl2 gas mixing ratios. [ABSTRACT FROM AUTHOR]

LaNiO3 (LNO) electrode was intensively studied as electrodes because LNO has a pseudocubic perovskite crystal structure with a lattice parameter of 3.84 Å. But the etching process of LNO thin films must be developed in order to realize highly integrated ferroelectric random access memories. In this work, we investigated etching characteristics and mechanisms of LNO thin films using inductively coupled BCl3/Ar plasma (ICP) system. The maximum etch rate of LNO thin films was 41.1 nm/min at a BCl3(20)/Ar(80) gas mixing ratio. The positive ions and the ion energy distributions were measured with a quadrupole mass spectrometer (QMS). As rf power and dc bias voltage increased and working pressure decreased, the ion energy and etch rates of LNO thin films were increased. A chemically assisted physical etch of LNO was experimentally confirmed by ICP system and QMS measurements. [ABSTRACT FROM AUTHOR]

The development of anisotropic etching process for (Pb,Sr)TiO3 (PST) thin films is an important task to provide a small feature size and an accurate pattern transfer. Etching characteristics of PST thin films were investigated using inductively coupled plasma etching system as functions of Cl2/Ar gas mixing ratio. The PST etch rate increased with the increase of chlorine radical and ion energy intensity. It was found that the increasing of Ar content in gas mixture lead to sufficient increasing of etch rate. The maximum etch rate of PST film is 56.2 nm/min at Cl2/(Cl2+Ar) of 0.2. It was proposed that the sputter etching is a dominant etching mechanism while the contribution of chemical reaction is relatively low due to low volatility of etching products. [ABSTRACT FROM AUTHOR]

ZrO2 thin films were investigated by surface characterization in a Cl2/Ar gas mixture adaptively coupled plasma system. The plasmas were characterized by optical emission spectroscopy analysis. The crystal structures of the films etched with gases at various mixing ratios were observed by X-ray diffraction. The results can show the damage caused by ion bombardment and chemical reaction of plasma on the crystalline structure of the ZrO2 surface. The chemical reactions of the etched ZrO2 films were investigated by angle-resolved X-ray photoelectron spectroscopy. The etching mechanism of ZrO2 thin films could be explained as Zr interacting with the Cl radical upon adding Cl2, but remaining at the surface owing to the low volatility of ZrClx. From the experimental results, the etching mechanism of ZrO2 was described as ion-assisted chemical reaction. [ABSTRACT FROM AUTHOR]